Improving solution times for stable matching problems through preprocessing

William Pettersson*, Maxence Delorme, Sergio García, Jacek Gondzio, Joerg Kalcsics, David Manlove

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We present new theory, heuristics, and algorithms for preprocessing instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and the Hospitals/Residents problem with Ties (HRT). Instances of these problems can be preprocessed by removing from the preference lists of some agents entries such that the set of stable matchings is not affected. Removing such entries reduces the problem size, creating smaller models that can be more easily solved by integer programming (IP) solvers. The new theorems are the first to describe when preference list entries can be removed from instances of HRT when ties are present on both sides, and also extend existing results on preprocessing instances of SMTI. A number of heuristics, as well as an IP model and a graph-based algorithm, are presented to find and perform this preprocessing. Experimental results show that our new graph-based algorithm achieves a 44% reduction in the average running time to find a maximum weight stable matching in real-world instances of SMTI compared to existing preprocessing techniques, and 80% compared to not using preprocessing. We also show that, when solving MAX-HRT instances with ties on both sides, our new techniques can reduce runtimes by up to 55%.

Original languageEnglish
Article number105128
JournalComputers and Operations Research
Volume128
DOIs
Publication statusPublished - Apr 2021
Externally publishedYes

Keywords

  • Hospital/Residents problem
  • Preprocessing
  • Stable Marriage problem
  • Ties and Incomplete Lists

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